Atomic Energy Levels Research Articles

Enabling Molecular-Level Computational Description of Redox and Proton-Coupled Electron Transfer Reactions of Samarium Diiodide.

Samarium diiodide (SmI2, Kagan's reagent) is a one-electron reductant with applications ranging from organic synthesis to nitrogen fixation. Highly inaccurate relative energies of redox and proton-coupled electron transfer (PCET) reactions of Kagan's reagent are predicted by pure and hybrid density functional approximations (DFAs) when only scalar relativistic effects are accounted for. Calculations including spin-orbit coupling (SOC) show that the SOC-induced differential stabilization of the Sm(III) versus the Sm(II) ground state is little affected by ligands and solvent, and a standard SOC correction derived from atomic energy levels is thus included in the reported relative energies. With this correction, selected meta-GGA and hybrid meta-GGA functionals predict Sm(III)/Sm(II) reduction free energies to within 5 kcal/mol of the experiment. Considerable discrepancies remain, however, in particular for the PCET-relevant O-H bond dissociation free energies, for which no regular DFA is within 10 kcal/mol of the experiment or CCSD(T). The main cause behind these discrepancies is the delocalization error, which leads to excess ligand-to-metal electron donation and destabilizes Sm(III) versus Sm(II). Fortunately, static correlation is unimportant for the present systems, and the error may be reduced by including information from virtual orbitals via perturbation theory. Contemporary, parametrized double-hybrid methods offer promise as companions to experimental campaigns in the further development of the chemistry of Kagan's reagent.

Proton Electric Charge Radius from Lepton Scattering

A proton is a bound state of a strong interaction, governed by Quantum Chromodynamics (QCD). The electric charge radius of a proton, denoted by rEp, characterizes the spatial distribution of its electric charge carried by the quarks. It is an important input for bound-state Quantum Electrodynamic (QED) calculations of the hydrogen atomic energy levels. However, physicists have been puzzled by the large discrepancy between rEp measurements from muonic hydrogen spectroscopy and those from ep elastic scattering and ordinary hydrogen spectroscopy for over a decade. Tremendous efforts, both theoretical and experimental, have been dedicated to providing various insights into this puzzle, but certain issues still remain unresolved, particularly in the field of lepton scatterings. This review will focus on lepton-scattering measurements of rEp, recent theoretical and experimental developments in this field, as well as future experiments using this technique.

Finite-nuclear-size effect in hydrogenlike ions with relativistic nuclear structure

The finite-nuclear-size (FNS) effect has a large contribution to atomic spectral properties, especially for heavy nuclei. By adopting the microscopic nuclear charge-density distributions obtained from the relativistic continuum Hartree-Bogoliubov (RCHB) theory, we systematically investigate the FNS corrections to atomic energy levels and bound-electron $g$ factors of hydrogenlike ions with nuclear charge up to 118. The comparison of the present numerical calculations with the predictions from empirical nuclear charge models, the nonrelativistic Skyrme-Hartree-Fock calculations, and the results based on experimental charge densities indicate that both the nuclear charge radius and the detailed shape of the charge-density distribution play important roles in determining the FNS corrections. The variation of FNS corrections to energy levels and $g$ factors with respect to the nuclear charge are investigated for the several lowest bound states of hydrogenlike ions. It is shown that they both increase by orders of magnitude with increasing nuclear charge, while the ratio between them has a relatively weak dependence on the nuclear charge. The FNS corrections to the ${s}_{1/2}$ and ${p}_{1/2}$ bound-state energies from the RCHB calculations are generally in good agreement with the analytical estimations by Shabaev [V. M. Shabaev, J. Phys. B 26, 1103 (1993)] based on the homogeneously charged sphere nuclear model, with the discrepancy indicating the distinct contribution of microscopic nuclear structure to the FNS effects.

Extending bandwidth sensitivity of Rydberg-atom-based microwave electrometry using an auxiliary microwave field

We demonstrate the use of an auxiliary microwave field to extend the bandwidth sensitivity of Rydberg-atom-based microwave electrometry. Electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting in Rydberg atom microwave electrometry provide advantageous sensitivity for the resonant detection of microwave (MW) fields because the Stark shift of the target Rydberg state takes the linear form of AT splitting. However, the sensitivity is reduced by several orders of magnitude for detuned MW fields because the Stark shift of the target Rydberg state depends on a weak nonlinear effect. We show that the auxiliary microwave field with appropriate Rabi frequency or detuning could shift the atomic energy levels to bring a particular Rydberg-Rydberg transition of interest for microwave sensing into resonance with the target microwave field. Using the atomic superheterodyne method, we verified the general method that regulates Rydberg energy levels using an auxiliary microwave field. The experimental results of this study confirm that this technique works efficiently for detecting microwave fields detuned by up to 100 MHz from resonance with the field-free Rydberg-Rydberg transition used for sensing. The measurement sensitivity of the detuned target field is increased by a factor of 10 compared with that achieved without the application of the auxiliary dressing field.

Toward XUV frequency comb spectroscopy of the 1 S–2 S transition in hbox {He}^+

The energy levels of hydrogen-like atoms and ions are accurately described by bound-state quantum electrodynamics (QED). hbox {He}^{+} ions have a doubly charged nucleus, which enhances the higher-order QED contributions and makes them interesting for precise tests of QED. Systematic effects that currently dominate the uncertainty in hydrogen spectroscopy, such as the second-order Doppler shift and time-of-flight broadening, are largely suppressed by performing spectroscopy on trapped and cooled hbox {He}^{+} ions. Measuring a transition in hbox {He}^{+} will extend the test of QED beyond the long-studied hydrogen. In this article, we describe our progress toward precision spectroscopy of the 1 S–2 S two-photon transition in hbox {He}^{+}. The transition can be excited by radiation at a wavelength of 60.8 nm generated by a high-power infrared frequency comb using high-order harmonic generation (HHG). The hbox {He}^{+} ions are trapped in a Paul trap and sympathetically cooled with laser-cooled hbox {Be}^{+} ions. Our recently developed signal detection scheme based on secular-scan spectrometry is capable of detecting hbox {He}^{+} excitation with single-event sensitivity.Graphic abstract

Nuclear Energy Levels in 44Ca using FPD6pn Interaction

Nuclear energy levels; total angular moment, even-even parity, and even odd parities for nucleons that were present outside closed core for the isobars 44Ca nuclei, which occupied low levels fp-LS shell (1f7/2,1f5/2, 2p3/2,2p1/2), within shell model calculations had been studied. The interaction has been used to calculate the nuclear energy levels which are fpd6pnwith fp shell model space. The results are compared with each other and with available experimental data, its agreement with some results is clear. All inscriptions are given in diagrammatic notation., the wave vectors and analysis are modeled in the so-called diagrammatic notation. The potential of the oscillator is utilized to construct a single particle vector, considered as a core. The OXFORD BEUNES AIRES SHELL MODEL CODE (OXBASH) is utilized to accomplish the results for all tested nuclei, the results as illustrated in figure (1) revealing that the levels have somehow consisted especially below 4 MeV, and the order are arranged similarly to the experimental scheme. All the states inherent above 4MeV are shifted especially for the odd values of total spin (J), so the model and interaction need to be modified.

FP Shell Effective Interactions and Nuclear Shell Structure of 44Sc

Abstract: Nuclear energy levels in 44Sc isotope, with fp shell model space occupation low levels fp-LS shell within shell model calculations had been investigated. The interactions has been used to calculate the nuclear energy levels which are fpd6, hw, fpy, with fp shell model space, d3f7cospn for 1d3/21f7/2 model space. The results are compared with each other and with available experimental data, its agreement with some results are clear. The used of model space interactions is the best fitted two body matrix elements in fp shell model space beside the good agreements in the reproduced values of energy levels scheme. The general estimation of the reproduced data are good especially below 3MeV. All inscriptions are given in diagrammatic notation, the wave vectors and analysis are modeled in the so called diagrammatic notation. The potential of oscillator is utilized to construct single particle vector, considering (_20^40)〖Ca〗_20 as a core for fp shell model space and (_16^32)S_(16 ) as an inert core for the model space d3f7. The OXFORD BEUNES AIRES SHELL MODEL CODE is utilized to accomplish the results for all tested nuclei.

An Energy Level with Principal Quantum Number n=0 Exists in a Hydrogen Atom

The classical quantum theory of Bohr does not take the theory of relativity into account. The energy levels of a hydrogen atom, derived by Bohr, are known to be approximations. In this paper, the kinetic energy and momentum of an electron in a hydrogen atom are reated relativistically. This paper predicts the existence of an n=0 energy level present in a hydrogen atom. However, the state where n=0 is not an energy level of the electron comprising the hydrogen atom. It is thought that an electron in the n=0 state forms a pair with a positron, and constitutes the vacuum inside the hydrogen atom.

Updated evaluation of potential ultralow Q -value β -decay candidates

"Ultra-low" Q value $\beta$ decays are referred to as such due to their low decay energies of less than $\sim$1 keV. Such a low energy decay is possible when the parent nucleus decays into an excited state in the daughter, with an energy close to that of the Q value. These decays are of interest as potential new candidates for neutrino mass determination experiments and as a testing ground for studies of atomic interference effects in the nuclear decay process. In this paper, we provide an updated evaluation of atomic mass data and nuclear energy level data to identify potential ultra-low Q value $\beta$ decay candidates. For many of these candidates, more precise and accurate atomic mass data is needed to determine if the Q value of the potential ultra-low decay branch is energetically allowed and in fact ultra-low. The precise atomic mass measurements can be achieved via Penning trap mass spectrometry.

Hyperfine structure investigations of the odd-parity electronic levels of the terbium atom

In the present work the hyperfine structure constants A and B were determined for 26 odd-parity energy levels of the terbium atom. Altogether 62 spectral lines in the spectral range between 483 - 538 nm were examined, using the method of laser induced fluorescence in a hollow cathode discharge lamp. All the results are presented for the first time. Additionally, the constants for 4 even-parity energy levels, previously reported by our research group, were reevaluated and slightly corrected.

Recoil Corrections to the Energy Levels of Hydrogenic Atoms.

We have completed the calculation of pure-recoil corrections of order (Zα)^{6} to Coulombic bound states of two spin-1/2 fermions without approximation in the particle masses. Our result applies to systems of arbitrary mass ratio such as muonium and positronium, as well as hydrogen and muonic hydrogen (with the neglect of proton structure effects). We have shown how the two-loop master integrals that occur in the relativistic region can be computed in analytic form and suggest that the same method can be applied to the three-loop integrals that would be present in a calculation of order (Zα)^{7} corrections.

Insight into materials science from a reductionist perspective

<p>The intricate correlation between structure and functionality in materials poses a significant challenge that has long been the subject of study. A reductionist approach to materials science necessitates comprehensive understanding, ranging from the precise solutions of atomic energy levels to the underlying principles of phase energy bands under specific boundary conditions, and up to macroscopic properties of materials that may be comprehended statistically. This study systematically dissects the macroscopic material into its components: phase, unit cell, atom, and electron, thus delving into material properties from the perspective of elementary particles. Our primary focus lies on the band structure (electron) and dispersion relation (phonon) in reciprocal space, and the distribution of four fundamental degrees of freedom (lattice, charge, orbital, spin) in real space. We utilize the Lithium-ion battery system as a case study to illustrate how reductionism can enrich our understanding of the materials at play. The paper concludes with a forward-looking reflection on the potential future trajectory and fundamental challenges of materials science using a reductionist approach.</p>

Simulation of lutetium metal evaporation with considering atomic metastable state

Lutetium-177, one of the current global research hotspots for medical isotopes, can be produced by reactor irradiation of lutetium-176, which can be produced and processed with the assistance of the electron beam physical vapor deposition (EB-PVD). The metal evaporation process is an important part of EB-PVD, which aims to convert solid metal into metal atomic vapor. The distribution of each macroscopic characteristic quantity, such as thermal population distribution, density distribution, velocity distribution, and temperature distribution of metal atomic vapor, will directly affect the utilization of metal vapor atoms, the subsequent deposition process, and coating process. In this paper, two-dimensional model and three-dimensional model of the metal evaporation process are established based on the direct simulation Monte Carlo method, and atomic metastable state is introduced into the collision assumption. The macroscopic characteristic quantities, such as the number density of metal atomic vapor, the motion velocity and the discrete degree of the total motion velocity in the evaporation process with or without considering the lutetium atomic metastable state, are analyzed and compared. The spatial distribution characteristics of each energy level of metal atomic vapor are observed, and the variation characteristics of the macroscopic characteristic quantities in the center with the slit opening size and the evaporation source surface temperature are discussed. The study results show that the number density of metal vapor passing through the beam flow device decreases, the average velocity in the <i>x</i>-direction and <i>z</i>-direction and the discrete degree of the total motion velocity increase, with the atomic metastable state taken into consideration. The beam flow device intensifies the transformation of the atomic energy level of the metal vapor and changes the physical parameters of the metal atomic vapor. At the same time, the slit opening size and the evaporation source surface temperature trigger off the change of the macroscopic characteristic quantity distribution of the metal vapor, including the degree of anomalous protrusion of each macroscopic characteristic quantity above the slit. The results of the three-dimensional simulation based on the two-dimensional model are consistent with the changes in the order of magnitude of data distribution and spatial distribution pattern, which can serve as a reference and guidance for the experimental study of the electron beam metal evaporation process.

Determination of the energies of new electronic levels of the holmium atom and investigation of their hyperfine structure

In the present work 27 electronic energy levels of the holmium atom, with previously unknown energies, were identified for the first time. Experimental data were acquired with the method of laser spectroscopy in a hollow cathode discharge lamp, with laser induced fluorescence detection. Recorded patterns for 79 spectral lines of holmium in the spectral range 485–535 nm enabled determination of the hyperfine structure constants A and B for 23 odd-parity levels and 11 even-parity levels. For 31 levels the results are presented for the first time. The energy values for the previously unknown levels were determined, too.

Identification of a potential ultralow- Q -value electron-capture decay branch in Se75 via a precise Penning trap measurement of the mass of As75

Background: Low energy $\beta$ and electron capture (EC) decays are important systems in neutrino mass determination experiments. An isotope with an ultra-low Q value $\beta$-decay to an excited state in the daughter with Qes < 1 keV could provide a promising alternative candidate for future experiments. $^{75}$Se EC and $^{75}$Ge $\beta$-decay represent such candidates, but a more precise determination of the mass of the common daughter, $^{75}$As, is required to evaluate whether their potential decay branches are energetically allowed and ultra-low. Purpose: Perform a precise atomic mass measurement of $^{75}$As and combine the result with the precisely known atomic masses of $^{75}$Se and $^{75}$Ge, along with nuclear energy level data for $^{75}$As to evaluate potential ultra-low Q value decay branches in the EC decay of $^{75}$Se and the $\beta$-decay of $^{75}$Ge. Method: The LEBIT Penning trap mass spectrometer at the Facility for Rare Isotope Beams was used to perform a high-precision measurement of the atomic mass of $^{75}$As via cyclotron frequency ratio measurements of $^{75}$As$^{+}$ to a $^{12}$C$_{6}^{+}$ reference ion. Results: The $^{75}$As mass excess was determined to be ME($^{75}$As)= -73 035.98(43) keV, from which the ground-state to ground-state Q values for $^{75}$Se EC and $^{75}$Ge $\beta$-decay were determined to be 866.50(44) keV and 1179.01(44) keV, respectively. These results were compared to energies of excited states in $^{75}$As at 865.4(5) keV and 1172.0(6) keV to determine Q values of 1.1(7) keV and 7.0(7) keV for the potential ultra-low EC and $\beta$-decay branches of $^{75}$Se and $^{75}$Ge, respectively. Conclusion: The $^{75}$Se EC decay to the 865.4 keV excited state in $^{75}$As is potentially ultra-low with Qes $\approx$ 1 keV. However, a more precise determination of the 865.4(5) keV level in $^{75}$As is required.

Optical Lines of Ru21+ to Ru24+ Ions

In this work, we report a spectroscopy measurement of Ru21+ to Ru24+ ions in the optical region using a low energy electron beam ion trap. Twelve lines were observed. The multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction methods were used to calculate the atomic level energies and the transition rates. With the assistance of the theoretical results, eleven magnetic dipole lines were identified. The experimental results provide new reference data for further theoretical investigations of the complex ions.

Processes of Current Transport in p-Si-n-(Si&lt;sub&gt;2&lt;/sub&gt;)&lt;sub&gt;1−&lt;/sub&gt;&lt;i&gt;&lt;sub&gt;y&lt;/sub&gt;&lt;/i&gt;&lt;sub&gt;−&lt;/sub&gt;&lt;i&gt;&lt;sub&gt;z&lt;/sub&gt;&lt;/i&gt;(GaP)&lt;i&gt;&lt;sub&gt;y&lt;/sub&gt;&lt;/i&gt;(ZnSe)&lt;i&gt;&lt;sub&gt;z&lt;/sub&gt;&lt;/i&gt; Heterostructure Produced by Liquid Phase Epitaxy

The possibility of growing multicomponent epitaxial films of a semiconductor solid solution of molecular substitution (Si2)1−y−z(GaP)y(ZnSe)z on Si and GaP substrates by liquid-phase epitaxy is shown. The distribution profiles of the atoms of the solid solution components Ga, P, Zn, Se, and Si over the thickness of the epitaxial film have been determined. The current-voltage (I−V) characteristics of p-Si-n-(Si2)1−y−z(GaP)y(ZnSe)z heterostructures have been studied. A temperature-independent I−V characteristic has been found, the existence of which is explained on the basis of a theory considering the possibility of "blurring" of the impurity level. By comparing the theoretical and experimental results, the half-width of the blurring band for the energy levels of atoms of Si2 and GaP molecules was determined, which had values equal to 0.146 and 0.34 eV, respectively.

Isotope shifts in cadmium as a sensitive probe for physics beyond the standard model

Isotope shifts (ISs) of atomic energy levels are sensitive probes of nuclear structure and new physics beyond the standard model. We present an analysis of the ISs of the cadmium atom (Cd I) and singly charged cadmium ion (Cd II). ISs of the 229 nm, 326 nm, 361 nm and 480 nm lines of Cd I are measured with a variety of techniques; buffer–gas-cooled beam spectroscopy, capturing atoms in a magneto-optic-trap, and optical pumping. IS constants for the D1 and D2 lines of Cd II are calculated with high accuracy by employing analytical response relativistic coupled-cluster theory in the singles, doubles and triples approximations. Combining the calculations for Cd II with experiments, we infer IS constants for all low-lying transitions in Cd I. We benchmark existing calculations via different many-body methods against these constants. Our calculations for Cd II enable nuclear charge radii of Cd isotopes to be extracted with unprecedented accuracy. The combination of our precise calculations and measurements shows that King plots for Cd I can improve the state-of-the-art sensitivity to a new heavy boson by up to two orders of magnitude.

Self-energy correction to the energy levels of heavy muonic atoms

The fully relativistic calculations of the self-energy correction to the fine-structure levels of heavy muonic atoms for the ground and first excited states are presented. Additionally, nuclear-model dependence as well as numerical convergence issues are discussed.

Water induced ultrathin Mo2C nanosheets with high-density grain boundaries for enhanced hydrogen evolution

Grain boundary controlling is an effective approach for manipulating the electronic structure of electrocatalysts to improve their hydrogen evolution reaction performance. However, probing the direct effect of grain boundaries as highly active catalytic hot spots is very challenging. Herein, we demonstrate a general water-assisted carbothermal reaction strategy for the construction of ultrathin Mo2C nanosheets with high-density grain boundaries supported on N-doped graphene. The polycrystalline Mo2C nanosheets are connected with N-doped graphene through Mo–C bonds, which affords an ultra-high density of active sites, giving excellent hydrogen evolution activity and superior electrocatalytic stability. Theoretical calculations reveal that the dz2 orbital energy level of Mo atoms is controlled by the MoC3 pyramid configuration, which plays a vital role in governing the hydrogen evolution activity. The dz2 orbital energy level of metal atoms exhibits an intrinsic relationship with the catalyst activity and is regarded as a descriptor for predicting the hydrogen evolution activity.